X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=6a9a8e5edd9ee62907a1486e29c25b334bedc041;hb=6c6ca17ba52b570cc50c1a9546ee9b6a5d3266fd;hp=6d360e2c103d61cc6b41a9cc3873f52db756e169;hpb=6fb9ab6b6068870323e996da931fc04c7710e3e4;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 6d360e2..6a9a8e5 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,21 +4,36 @@
 module Grid
 where
 
-import Cube (Cube(Cube))
+import qualified Data.Array.Repa as R
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
+import Cube (Cube(Cube), find_containing_tetrahedra)
 import FunctionValues
+import Point (Point)
+import ScaleFactor
+import Tetrahedron (polynomial)
+import Values (Values3D, dims, empty3d, zoom_shape)
+
 
 -- | Our problem is defined on a Grid. The grid size is given by the
 --   positive number h. The function values are the values of the
 --   function at the grid points, which are distance h from one
 --   another in each direction (x,y,z).
 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
-                   function_values :: [[[Double]]] }
+                   function_values :: Values3D }
           deriving (Eq, Show)
 
 
+instance Arbitrary Grid where
+    arbitrary = do
+      (Positive h') <- arbitrary :: Gen (Positive Double)
+      fvs <- arbitrary :: Gen Values3D
+      return (make_grid h' fvs)
+
+
 -- | The constructor that we want people to use. If we're passed a
 --   non-positive grid size, we throw an error.
-make_grid :: Double -> [[[Double]]] -> Grid
+make_grid :: Double -> Values3D -> Grid
 make_grid grid_size values
     | grid_size <= 0 = error "grid size must be positive"
     | otherwise = Grid grid_size values
@@ -26,22 +41,104 @@ make_grid grid_size values
 
 -- | Creates an empty grid with grid size 1.
 empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
-
+empty_grid = Grid 1 empty3d
 
 
--- This is how we do a 'for' loop in Haskell.
--- No, seriously.
+-- | Returns a three-dimensional list of cubes centered on the grid
+--   points of g with the appropriate 'FunctionValues'.
 cubes :: Grid -> [[[Cube]]]
 cubes g
-    | fvs == [[[]]] = [[[]]]
-    | head fvs == [[]] = [[[]]]
+    | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
     | otherwise =
         [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
               | j <- [0..ysize]]
               | k <- [0..zsize]]
     where
       fvs = function_values g
-      zsize = (length fvs) - 1
-      ysize = (length $ head fvs) - 1
-      xsize = (length $ head $ head fvs) - 1
+      (xsize, ysize, zsize) = dims fvs
+
+
+-- | Takes a grid and a position as an argument and returns the cube
+--   centered on that position. If there is no cube there (i.e. the
+--   position is outside of the grid), it will throw an error.
+cube_at :: Grid -> Int -> Int -> Int -> Cube
+cube_at g i j k
+    | i < 0 = error "i < 0 in cube_at"
+    | j < 0 = error "j < 0 in cube_at"
+    | k < 0 = error "k < 0 in cube_at"
+    | otherwise =
+        let zsize = length (cubes g) in
+          if k >= zsize then
+            error "k >= xsize in cube_at"
+          else
+            let ysize = length ((cubes g) !! k) in
+              if j >= ysize then
+                error "j >= ysize in cube_at"
+              else
+                let xsize = length (((cubes g) !! k) !! j) in
+                  if i >= xsize then
+                    error "i >= xsize in cube_at"
+                  else
+                    (((cubes g) !! k) !! j) !! i
+
+
+--   The first cube along any axis covers (-h/2, h/2). The second
+--   covers (h/2, 3h/2).  The third, (3h/2, 5h/2), and so on.
+--
+--   We translate the (x,y,z) coordinates forward by 'h/2' so that the
+--   first covers (0, h), the second covers (h, 2h), etc. This makes
+--   it easy to figure out which cube contains the given point.
+calculate_containing_cube_coordinate :: Grid -> Double -> Int
+calculate_containing_cube_coordinate g coord
+    -- Don't use a cube on the boundary if we can help it. This
+    -- returns cube #1 if we would have returned cube #0 and cube #1
+    -- exists.
+    | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1
+    | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
+    where
+      (xsize, ysize, zsize) = dims (function_values g)
+      cube_width = (h g)
+      offset = cube_width / 2
+
+
+-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
+--   Since our grid is rectangular, we can figure this out without having
+--   to check every cube.
+find_containing_cube :: Grid -> Point -> Cube
+find_containing_cube g p =
+    cube_at g i j k
+    where
+      (x, y, z) = p
+      i = calculate_containing_cube_coordinate g x
+      j = calculate_containing_cube_coordinate g y
+      k = calculate_containing_cube_coordinate g z
+
+
+{-# INLINE zoom_lookup #-}
+zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup g scale_factor _ = zoom_result g scale_factor
+
+
+{-# INLINE zoom_result #-}
+zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
+zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
+  f p
+  where
+    i' = (fromIntegral i) / (fromIntegral sfx)
+    j' = (fromIntegral j) / (fromIntegral sfy)
+    k' = (fromIntegral k) / (fromIntegral sfz)
+    p  = (i', j', k') :: Point
+    c = find_containing_cube g p
+    t = head (find_containing_tetrahedra c p)
+    f = polynomial t
+
+
+zoom :: Grid -> ScaleFactor -> Values3D
+zoom g scale_factor
+    | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+    | otherwise =
+        R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
+          where
+            arr = function_values g
+            (xsize, ysize, zsize) = dims arr
+            transExtent = zoom_shape scale_factor